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The uplink of a space-time spreading code-division multiple-access system with dual transmit and dual receive antennas is analyzed with the effect of imperfect channel estimation. With the help of pilot signals, the Rayleigh multipath fading channel experienced by the transmitted signal is estimated by simple correlators, and subsequently used to coherently combine the multipath signals in a RAKE-like space-time combiner. As a system becomes more wideband, more multipaths are resolved, and the energy in each path is reduced. This reduction in signal strength causes increased estimation error and impacts the system performance. Through the derivation of the probability of error in a space-time spreading system with channel-estimation errors, this paper studies the tradeoff between diversity and estimation errors. It is shown that an optimal bandwidth exists and the optimal power allocation for the pilot signals is a function of the quality of the channel estimates.